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Reliability of a Space Launch

Model a launch into space in three phases: a ground check, a launch phase, and in orbit. The three phases have environmental harshness factors of 5400 and 1.

Wolfram Language code: {Subscript[𝒟, oGuidance], Subscript[𝒟, iGuidance], Subscript[𝒟, oIgnition], Subscript[𝒟, iIgnition], Subscript[𝒟, oSeparation], Subscript[𝒟, iSeparation], Subscript[𝒟, oPower], Subscript[𝒟, oCom], Subscript[𝒟, iCom], Subscript[𝒟, oInstrument], Subscript[𝒟, iInstrument], Subscript[𝒟, oPropulsion], Subscript[𝒟, structure]} = ExponentialDistribution[k # / 1000]& /@ {0.01, 0.0001, 0.1, 0.001, 0.01, 0.0001, 0.02, 0.05, 0.0005, 0.01, 0.0005, 0.05, 0.001};
Wolfram Language code: ground = guidance1∧guidance2∧ignition1A∧ignition1B∧ignition2A∧ignition2B∧separation1∧separation2∧powerA∧powerB∧comA∧comB∧instrumentA∧instrumentB∧structure; Subscript[ℛ, ground] = ReliabilityDistribution[ground, {{guidance1, Subscript[𝒟, iGuidance]}, {guidance2, Subscript[𝒟, iGuidance]}, {ignition1A, Subscript[𝒟, iIgnition]}, {ignition1B, Subscript[𝒟, iIgnition]}, {ignition2A, Subscript[𝒟, iIgnition]}, {ignition2B, Subscript[𝒟, iIgnition]}, {separation1, Subscript[𝒟, iSeparation]}, {separation2, Subscript[𝒟, iSeparation]}, {powerA, Subscript[𝒟, oPower]}, {powerB, Subscript[𝒟, oPower]}, {comA, Subscript[𝒟, iCom]}, {comB, Subscript[𝒟, iCom]}, {instrumentA, Subscript[𝒟, iInstrument]}, {instrumentB, Subscript[𝒟, oInstrument]}, {structure, Subscript[𝒟, structure]}} /. k -> 5];
Wolfram Language code: launch = guidance1∧guidance2∧(ignition1A∨ignition1B)∧propulsion1∧separation1∧(ignition2A∨ignition2B)∧propulsion2∧separation2∧(powerA∨powerB)∧(comA∨comB)∧instrumentA∧instrumentB∧structure; Subscript[ℛ, launch] = ReliabilityDistribution[launch, {{guidance1, Subscript[𝒟, oGuidance]}, {guidance2, Subscript[𝒟, iGuidance]}, {ignition1A, Subscript[𝒟, oIgnition]}, {ignition1B, Subscript[𝒟, oIgnition]}, {ignition2A, Subscript[𝒟, oIgnition]}, {ignition2B, Subscript[𝒟, oIgnition]}, {separation1, Subscript[𝒟, oSeparation]}, {separation2, Subscript[𝒟, oSeparation]}, {powerA, Subscript[𝒟, oPower]}, {powerB, Subscript[𝒟, oPower]}, {comA, Subscript[𝒟, oCom]}, {comB, Subscript[𝒟, oCom]}, {instrumentA, Subscript[𝒟, oInstrument]}, {instrumentB, Subscript[𝒟, iInstrument]}, {structure, Subscript[𝒟, structure]}, {propulsion1, Subscript[𝒟, oPropulsion]}, {propulsion2, Subscript[𝒟, oPropulsion]}} /. k -> 400];
Wolfram Language code: orbit = guidance2∧(powerA∨powerB)∧(comA∨comB)∧instrumentB∧structure; Subscript[ℛ, orbit] = ReliabilityDistribution[orbit, {{guidance2, Subscript[𝒟, oGuidance]}, {powerA, Subscript[𝒟, oPower]}, {powerB, Subscript[𝒟, oPower]}, {comA, Subscript[𝒟, oCom]}, {comB, Subscript[𝒟, oCom]}, {instrumentB, Subscript[𝒟, oInstrument]}, {structure, Subscript[𝒟, structure]}} /. k -> 1];
Wolfram Language code: rel = SurvivalFunction[Subscript[ℛ, ground], 24] * SurvivalFunction[Subscript[ℛ, launch], 0.1] * SurvivalFunction[Subscript[ℛ, orbit], 100 * 24];
Wolfram Language code: plotOpts = {PlotRange -> {0, 1}, Filling -> Axis, Ticks -> None, ImageSize -> 150, PlotRangePadding -> 0}; Grid[{{"", "Ground", "Launch", "Orbit"}, {Rotate["SurvivalFunction", π / 2], Plot[SurvivalFunction[Subscript[ℛ, ground], t], {t, 0, 15000}, Evaluate@plotOpts, FillingStyle -> ColorData["Crayola"]["Mahogany"]], Plot[SurvivalFunction[Subscript[ℛ, launch], t], {t, 0, 40}, Evaluate@plotOpts, FillingStyle -> Orange], Plot[SurvivalFunction[Subscript[ℛ, orbit], t], {t, 0, 50000}, Evaluate@plotOpts, FillingStyle -> ColorData["Crayola"]["Inchworm"]]}, {Rotate["MTTF", π / 2], Mean[Subscript[ℛ, ground]], Mean[Subscript[ℛ, launch]], Mean[Subscript[ℛ, orbit]]}, {Rotate["Mission time", π / 2], 24, 0.1, 100 * 24}, {Rotate["Reliability", π / 2], SurvivalFunction[Subscript[ℛ, ground], 24], SurvivalFunction[Subscript[ℛ, launch], 0.1], SurvivalFunction[Subscript[ℛ, orbit], 100 * 24]}, {Item["Mission reliability:", Background -> StandardBlue], SpanFromLeft, Item[rel, Background -> StandardBlue], SpanFromLeft}}, Frame -> All, Spacings -> {1, 2}, BaseStyle -> {FontFamily -> "Verdana", FontSize -> 12}]